Does God Collapse the Wave Function?

In order to understand how the Schrödinger Wave Equation
relates to reality, we could postulate a transcendent world observer - a divine
mind whose observations collapse the wave functions on our behalf. In effect
this would be the quantum-mechanical version of Bishop Berkeleys idealism.
This is memorably summarised in a couple of limericks:

There was once a man who
said God
Must think it exceedingly odd
If he finds that this tree
Continues to be
When theres no one about in the quad.

And the reply:

Dear Sir, Your
astonishments odd:
I am always about in the quad.
And thats why the tree
Will continue to be,
Since observed by Yours faithfully, God.

The problem with this attractive solution to the measurement
problem is that it proves too much. Invoking a divine observer leads to the
question of why there should be any quantum measurement problem at all. Why
should anything be left indeterminate for us to determine by our measurements?
Is God only interested in those aspects of creation that are above a certain
size?